تقرير
Transformation properties of Andrews-Beck $NT$ functions and generalized Appell-Lerch series
| العنوان: | Transformation properties of Andrews-Beck $NT$ functions and generalized Appell-Lerch series |
|---|---|
| المؤلفون: | Chen, Rong, Zhu, Xiao-Jie |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, Mathematics - Combinatorics, Primary 11P84, Secondary 05A17, 11F11, 11F30, 11F37, 11P83 |
| الوصف: | In 2021, Andrews mentioned that George Beck introduced a partition statistic $NT(r,m,n)$ which is related to Dyson's rank statistic. Motivated by Andrews's work, scholars have established a number of congruences and identities involving $NT(r,m,n)$. In this paper, we strengthen and extend a recent work of Mao on the transformation properties of the $NT$ function and provide an analogy of Hickerson and Mortenson's work on the rank function. As an application, we demonstrate how one can deduce from our results many identities involving $NT(r,m,n)$ and another crank-analog statistic $M_\omega(r,m,n)$. As a related result, some new properties of generalized Appell-Lerch series are given. Comment: 47 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.20790 |
| رقم الأكسشن: | edsarx.2407.20790 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |